What are these white bits in my mesh?
I've done my best to recreate your issue, I think you've created several n-gons here, and the artifact you're seeing is Blender triangulating that n-gon.

You can create better topology in a somewhat automatic fashion by using a bevel on this corner.  I'll be starting over with a primitive cube, and I've just scaled up the bottom to create this tapered shape of yours.
Just select one edge and bevel it with the desired number of segments.

And then select the top corner's vertices and do a Merge At Center.


This has created a triangle for each segment of the corner.  Note that typically it is recommended to stick to 4-sided faces called quads, but the most important thing is to avoid n-gons unless you are looking for some very particular behavior.